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Dynamical properties of minimal Ferenczi subshifts

Part of: Topological dynamics Ergodic theory

Published online by Cambridge University Press:  22 February 2023

FELIPE ARBULÚ  and
FABIEN DURAND Open the ORCID record for FABIEN DURAND [Opens in a new window]
FELIPE ARBULÚ
Affiliation:
Laboratoire Amiénois de Mathématique Fondamentale et Apliquée, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens cedex 1, France (e-mail: felipe.arbulu@u-picardie.fr)
FABIEN DURAND*
Affiliation:
Laboratoire Amiénois de Mathématique Fondamentale et Apliquée, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens cedex 1, France (e-mail: felipe.arbulu@u-picardie.fr)
*
e-mail: fabien.durand@u-picardie.fr
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Abstract

We provide an explicit $\mathcal {S}$-adic representation of rank-one subshifts with bounded spacers and call the subshifts obtained in this way ‘minimal Ferenczi subshifts’. We aim to show that this approach is very convenient to study the dynamical behavior of rank-one systems. For instance, we compute their topological rank, the strong and the weak orbit equivalence class. We observe that they have an induced system that is a Toeplitz subshift having discrete spectrum. We also characterize continuous and non-continuous eigenvalues of minimal Ferenczi subshifts.

Keywords

Ferenczi subshiftsrank-one subshiftsS-adic subshiftsminimal Cantor systems

MSC classification

Primary: 37B10: Symbolic dynamics
Secondary: 37A05: Measure-preserving transformations

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 12 , December 2023 , pp. 3923 - 3970
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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